MHD flow between electromagnetically coupled concentric cylinders with slipping walls

Abstract

In this study, a fully developed, laminar Magnetohydrodynamic (MHD) flow between concentric cylinders with slipping walls is investigated. The induced magnetic field of the electrically conducting inner cylinder is also studied. The problem is considered on the 2D annular cross-section of the pipe. The inner disk and the fluid are electromagnetically coupled and the outer thin boundary is insulated. Both walls of the annulus are slipping with the same or different slip lengths. The flow is subjected to a horizontally applied uniform magnetic field. The system of governing equations is discretized by the Dual Reciprocity Boundary Element Method (DRBEM). The resultant matrix–vector equations are solved as a whole with coupled induced magnetic field conditions on the disk-fluid boundary. The effects of the slip, the Hartmann number (Ha) and the conductivity ratio are analyzed. Numerical results reveal the continuation of magnetic field through the disk in the no-slip case. An increase in the Ha forces the magnetic field isolines to close themselves in the annulus and decelerates the flow. The wall slip accelerates the flow and diminishes boundary layers near the slipping walls. As the inner wall slip length advances, a uniform flow develops between the cylinders. The slip at the outer wall separates the flow into two vortices and strengthens the influence of the Ha increase. When the fluid conductivity is larger than the disk conductivity, the inner wall starts to behave as if it was insulated and the slip at the same wall enhances this effect. The proposed numerical scheme is capable of capturing the MHD flow characteristics with the slip and the electromagnetically coupled wall conditions with less computational cost due to the boundary only nature of the DRBEM.